Without formula and process, it’s hard to know what has happened, but in general benzoyl peroxide (BPO) BPO is not very soluble in water. When you dissolve it in ethyl alcohol, it may not be completely mixed into the water-based part of your face wash, potentially creating a suspension. This could cause it to look creamy or opaque (I think it’s bc the crystals would scatter light? that’s my understand but could be wrong).
But for viscosity loss, alcohol is a solvent and can always affect the performance of the surfactants in a system, so this could easily be the cause of the viscosity loss.
I would try using a solubiliser to help incorporate the BPO, like PEG-40 hydrogenated castor oil. I would also look at the concentration % of alcohol in the formula as it could be causing the viscosity loss. Is your rheology modifier compatible with alcohol? not all are.
As said, without formula and process, this is just guessing but might help you to work through what is happening.